Apparently, US patent law distinguishes things that are discovered from things that are invented, and allows patents only of the latter. You cannot, for example, find a beautiful shell on a beach, and take out a patent to prevent other people from being able to copy its design without first paying you a fee. If, on the other hand, you come up with a novel and ingenious way to build a can opener out of formaldehyde and steel, then, assuming you follow correct procedures for establishing and protecting your idea, then you are entitled to ask other people for some sort of financial acknowledgement before they make use of it. So far, so reasonable.

However, many useful ideas do not fall so easily into one camp or the other. One example is a novel heavy element, created in a laboratory using a huge amount of energy to persuade protons and neutrons to fuse together into an atom that is not known to occur naturally, and which is so unstable it persists for only tiny fractions of a second. Another example would be a synthetic organism, of the sort built by Craig Venter's team. They would be novel life forms, in so far as they do not occur naturally. On the other hand, they are constructed by adding together components that are taken from, or copied from, other, naturally occurring, life forms. If you take some discovered things, and combine them in novel ways, have you therein invented something? What about sporks?!

Intriguingly, computer software is another, somewhat more prosaic example.At present, it cannot be patented, because the view is taken that: software is essentially a bundle of algorithms; algorithms are procedures for solving mathematical problems; and solutions to mathematical problems - mathematical truths - are discovered, not invented.

Mathematical nominalists would, of course, disagree. Maths nominalism is a philosophical position which holds that numbers and other abstract mathematical objects are cultural artefacts, created by humankind along with words, novels and sporks. They say that the number three is a more deeply entrenched and enduring idea than that of a spork, for sure, but we shouldn't let that mislead us into treating it as any sort of deep truth, predating humanity's existence. Threeness is in no sense necessary, say the nominalists.We might have skipped straight from two to four in our counting, or used 3.5 instead, or used a counting system that only recognised even numbers.

Platonists, the nominalists' adversaries, would say that even if humans had never hit upon the idea of the number three (perhaps we'd had only one finger on each hand, for example) the number itself would have existed no less, because it would still have been the answer to four minus one, or two plus one, even if all the numbers had different names, or if we counted differently, or if we failed to count altogether. Threeness, for a Platonist, has always existed, and in no sense depended on humans happening to evolve in order to recognise or discover its existence. There is no way that two things plus one more thing could ever amount to anything other than three things, they say.

For the moment, US patent law seems to be on the side of the Platonists. One wonders whether this oughtn't apply to many other ideas which Platonists would claim to be eternally, necessarily true. Music, for example, is largely derived from maths. Even art - surely the paradigm of created cultural artefacts - Plato might have said that beautiful statues achieve their status by closely approximating the shape of the forms. Yet we think of art artefacts as paradigmatic, well, artefacts,

As usual, in philosophy, things resist our attempts to put them in the neat categories required by law and patent clerks.

The item was based on a 2013 American Mathematical Society article by David A. Edwards.